asheinin/The_Mathematical_Principles_of_Natural_Philosophy_1846

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As, the mathematical signification of this word defined, 100
Attraction of all bodies demonstrated, 397
“ the certainty of this demonstration shewn, 384
“ the cause or manner thereof no where defined by the author, 507
“ the common centre of gravity of the earth, sun, and all the planets, is at rest, confirmed by Cor. 2, Prop. XIV, Book III, 401
“ the common centre of gravity of the earth and moon goes round the orbis magnus, 402
“ its distance from the earth and from the moon, 452
Centre, the common centre of gravity of many bodies does not alter its state of motion or rest by the actions of the bodies among themselves, 87
“ of the forces by which revolving bodies are retained in their orbits, how indicated by the description of areas, 107
“ how found by the given velocities of the revolving bodies, 110
Circle, by what law of centripetal force tending to any given point its circumference may be described, 108, 111, 114
Comets, a sort of planets, not meteors, 465, 486
“ higher than the moon, and in the planetary regions, 460
“ their distance how collected very nearly by observations, 461
“ more of them observed in the hemisphere towards the sun than in the opposite hemisphere; and how this comes to pass, 464
“ shine by the sun s light reflected from them, 464
“ surrounded with vast atmospheres, 463, 465
“ those which come nearest to the sun probably the least, 495
“ why they are not comprehended within a zodiac, like the planets, but move differently into all parts of the heavens, 502
“ may sometimes fall into the sun, and afford a new supply of fire, 502
“ the use of them hinted, 492
“ move in conic sections, having their foci in the sun s centre, and by radii drawn to the sun describe areas proportional to the times. Move in ellipses if they come round again in their orbits, but these ellipses will be near to parabolas, 466
Comet's parabolic trajectory found from three observations given, 472
“ corrected when found, 495
“ place in a parabola found to a given time, 466
“ velocity compared with the velocity of the planets, 466
Comets' Tails directed from the sun, 489
“ “ brightest and largest immediately after their passage through the neighbourhood of the sun, 487
“ “ their wonderful rarity, 490
“ “ their origin and nature, 463
“ “ in what space of time they ascend from their heads, 490
Comet of the years 1664 and 1665 — the observations of its motion compared with the theory, 496
“ of the years 1680 and 1681 — observations of its motion, 474
“ its motion computed in a parabolic orbit, 478
“ in an elliptic orbit, 479
“ its trajectory, and its tail in the several parts of its orbit, delineated, 484
“ of the year 1682 — its motion compared with the theory, 500
“ seems to have appeared in the year 1607, and likely to return again after a period of years, 501, 502
“ of the year 1683 — its motion compared with the theory, 499
“ of the year 1723 — its motion compared with the theory, 501
Conic Sections, by what law of centripetal force tending to any given point they may be described by revolving bodies, 125
“ the geometrical description of them when the foci are given, 125
“ when the foci are not given, 131
“ when the centres or asymptotes are given, 147
Curvature of figures how estimated, 271, 423
Curves distinguished into geometrically rational and geometrically irrational, 157
Cycloid, or Epicycloid, its rectification, 184
“ “ its evoluta, 185
Cylinder, the attraction of a cylinder composed of attracting particles, whose forces are reciprocally as the square of the distances, 239
Descent of heavy bodies in vacuo, how much it is, 405
“ and ascent of bodies in resisting mediums, 252, 265, 281, 283, 345
Descent or Ascent rectilinear, the spaces described, the times of decryption, and the velocities acquired in such ascent or descent, compared, on the supposition of any kind of centripetal force, 160
Earth, its dimension by Norwood, by Picart, and by Cassini, 405
“ its figure discovered, with the proportion of its diameters, and the measure of the degrees upon the meridian, 405, 409
“ the excess of its height at the equator above its height at the poles, 407, 412
“ its greatest and least semi-diameter, 407
“ its mean semi-diameter, 407
“ the globe of the earth more dense than if it was entirely water, 400
“ the nutation of its axis, 413
“ the annual motion thereof in the orbis magnus demonstrated, 498
“ the eccentricity thereof how much, 452
“ the motion of its aphelion how much, 404
Ellipses, by what law of centripetal force tending to the centre of the figure it is described by a revolving body, 114
“ by what law of centripetal force tending to the focus of the figure it is described by a revolving body, 116
Fluid, the definition thereof, 108
Fluids, the laws of their density and compression shewn, 293
“ their motion in running out at a hole in a vessel determined, 331
Forces, their composition and resolution, 84
“ attractive forces of spherical bodies, composed of particles attracting according to any law, determined, 218
“ attractive forces of bodies not spherical, composed of particles attracting according to any law, determined, 233
“ the invention of the centripetal forces, when a body is revolved in a non-resisting space about an immoveable centre in any orbit, 103, 116
“ the centripetal forces tending to any point by which any figure may be described by a revolving body being given, the centripetal forces tending to any other point by which the same figure may be described in the same periodic time are also given, 113
“ the centripetal forces by which any figure is described by a revolving body being given, there are given the forces by which a new figure may be described, if the ordinates are augmented or diminished in any given ratio, or the angle of their inclination be any how changed, the periodic time remaining the same, 116
“ centripetal forces decreasing in the duplicate proportion of the distances, what figures may be described by them, 120, 196
Force, centripetal force defined, 74
“ the absolute quantity of centripetal force defined, 75
“ the accelerative quantity of the same defined, 76
“ the motive quantity of the same defined, 76
“ the proportion thereof to any known force how collected, 109
“ a centripetal force that is reciprocally as the cube of the ordinate tending to a vastly remote centre of force will cause a body to move in any given conic section, 114
“ a centripetal force that is as the cube of the ordinate tending to a vastly remote centre of force will cause a body to move in an hyperbola, 243
“ centrifugal force of bodies on the earth s equator, how great, 405
God, his nature, 506
Gravity mutual between the earth and its parts, 94
“ of a different nature from magnetical force, 397
“ the cause of it not assigned, 507
“ tends towards all the planets, 393
“ from the surfaces of the planets upwards decreases in the duplicate ratio of the distances from the centre, 400
“ from the same downwards decreases nearly in the simple ratio of the same, 400
“ tends towards all bodies, and is proportional to the quantity of matter in each, 397
“ is the force by which the moon is retained in its orbit, 391
“ the same proved by an accurate calculus, 453
“ is the force by which the primary planets and the satellites of Jupiter and Saturn are retained in their orbits, 393
Heat, an iron rod increases in length by heat, 412
“ of the sun, how great at different distances from the sun, 486
“ how great in Mercury, 400
“ how great in the comet of 1680, when in its perihelion, 486
Heavens are void of any sensible resistance, 401, 445, 492; and, therefore, of almost any corporeal fluid whatever, 355, 356
“ suffer light to pass through them without any refraction, 485
Hydrostatics, the principles thereof delivered, 293

As, the mathematical signification of this word defined, 100

Attraction of all bodies demonstrated, 397

“ the certainty of this demonstration shewn, 384

“ the cause or manner thereof no where defined by the author, 507

“ the common centre of gravity of the earth, sun, and all the planets, is at rest, confirmed by Cor. 2, Prop. XIV, Book III, 401

“ the common centre of gravity of the earth and moon goes round the orbis magnus, 402

“ its distance from the earth and from the moon, 452

Centre, the common centre of gravity of many bodies does not alter its state of motion or rest by the actions of the bodies among themselves, 87

“ of the forces by which revolving bodies are retained in their orbits, how indicated by the description of areas, 107

“ how found by the given velocities of the revolving bodies, 110

Circle, by what law of centripetal force tending to any given point its circumference may be described, 108, 111, 114

Comets, a sort of planets, not meteors, 465, 486

“ higher than the moon, and in the planetary regions, 460

“ their distance how collected very nearly by observations, 461

“ more of them observed in the hemisphere towards the sun than in the opposite hemisphere; and how this comes to pass, 464

“ shine by the sun s light reflected from them, 464

“ surrounded with vast atmospheres, 463, 465

“ those which come nearest to the sun probably the least, 495

“ why they are not comprehended within a zodiac, like the planets, but move differently into all parts of the heavens, 502

“ may sometimes fall into the sun, and afford a new supply of fire, 502

“ the use of them hinted, 492

“ move in conic sections, having their foci in the sun s centre, and by radii drawn to the sun describe areas proportional to the times. Move in ellipses if they come round again in their orbits, but these ellipses will be near to parabolas, 466

Comet's parabolic trajectory found from three observations given, 472

“ corrected when found, 495

“ place in a parabola found to a given time, 466

“ velocity compared with the velocity of the planets, 466

Comets' Tails directed from the sun, 489

“ “ brightest and largest immediately after their passage through the neighbourhood of the sun, 487

“ “ their wonderful rarity, 490

“ “ their origin and nature, 463

“ “ in what space of time they ascend from their heads, 490

Comet of the years 1664 and 1665 — the observations of its motion compared with the theory, 496

“ of the years 1680 and 1681 — observations of its motion, 474

“ its motion computed in a parabolic orbit, 478

“ in an elliptic orbit, 479

“ its trajectory, and its tail in the several parts of its orbit, delineated, 484

“ of the year 1682 — its motion compared with the theory, 500

“ seems to have appeared in the year 1607, and likely to return again after a period of years, 501, 502

“ of the year 1683 — its motion compared with the theory, 499

“ of the year 1723 — its motion compared with the theory, 501

Conic Sections, by what law of centripetal force tending to any given point they may be described by revolving bodies, 125

“ the geometrical description of them when the foci are given, 125

“ when the foci are not given, 131

“ when the centres or asymptotes are given, 147

Curvature of figures how estimated, 271, 423

Curves distinguished into geometrically rational and geometrically irrational, 157

Cycloid, or Epicycloid, its rectification, 184

“ “ its evoluta, 185

Cylinder, the attraction of a cylinder composed of attracting particles, whose forces are reciprocally as the square of the distances, 239

Descent of heavy bodies in vacuo, how much it is, 405

“ and ascent of bodies in resisting mediums, 252, 265, 281, 283, 345

Descent or Ascent rectilinear, the spaces described, the times of decryption, and the velocities acquired in such ascent or descent, compared, on the supposition of any kind of centripetal force, 160

Earth, its dimension by Norwood, by Picart, and by Cassini, 405

“ its figure discovered, with the proportion of its diameters, and the measure of the degrees upon the meridian, 405, 409

“ the excess of its height at the equator above its height at the poles, 407, 412

“ its greatest and least semi-diameter, 407

“ its mean semi-diameter, 407

“ the globe of the earth more dense than if it was entirely water, 400

“ the nutation of its axis, 413

“ the annual motion thereof in the orbis magnus demonstrated, 498

“ the eccentricity thereof how much, 452

“ the motion of its aphelion how much, 404

Ellipses, by what law of centripetal force tending to the centre of the figure it is described by a revolving body, 114

“ by what law of centripetal force tending to the focus of the figure it is described by a revolving body, 116

Fluid, the definition thereof, 108

Fluids, the laws of their density and compression shewn, 293

“ their motion in running out at a hole in a vessel determined, 331

Forces, their composition and resolution, 84

“ attractive forces of spherical bodies, composed of particles attracting according to any law, determined, 218

“ attractive forces of bodies not spherical, composed of particles attracting according to any law, determined, 233

“ the invention of the centripetal forces, when a body is revolved in a non-resisting space about an immoveable centre in any orbit, 103, 116

“ the centripetal forces tending to any point by which any figure may be described by a revolving body being given, the centripetal forces tending to any other point by which the same figure may be described in the same periodic time are also given, 113

“ the centripetal forces by which any figure is described by a revolving body being given, there are given the forces by which a new figure may be described, if the ordinates are augmented or diminished in any given ratio, or the angle of their inclination be any how changed, the periodic time remaining the same, 116

“ centripetal forces decreasing in the duplicate proportion of the distances, what figures may be described by them, 120, 196

Force, centripetal force defined, 74

“ the absolute quantity of centripetal force defined, 75

“ the accelerative quantity of the same defined, 76

“ the motive quantity of the same defined, 76

“ the proportion thereof to any known force how collected, 109

“ a centripetal force that is reciprocally as the cube of the ordinate tending to a vastly remote centre of force will cause a body to move in any given conic section, 114

“ a centripetal force that is as the cube of the ordinate tending to a vastly remote centre of force will cause a body to move in an hyperbola, 243

“ centrifugal force of bodies on the earth s equator, how great, 405

God, his nature, 506

Gravity mutual between the earth and its parts, 94

“ of a different nature from magnetical force, 397

“ the cause of it not assigned, 507

“ tends towards all the planets, 393

“ from the surfaces of the planets upwards decreases in the duplicate ratio of the distances from the centre, 400

“ from the same downwards decreases nearly in the simple ratio of the same, 400

“ tends towards all bodies, and is proportional to the quantity of matter in each, 397

“ is the force by which the moon is retained in its orbit, 391

“ the same proved by an accurate calculus, 453

“ is the force by which the primary planets and the satellites of Jupiter and Saturn are retained in their orbits, 393

Heat, an iron rod increases in length by heat, 412

“ of the sun, how great at different distances from the sun, 486

“ how great in Mercury, 400

“ how great in the comet of 1680, when in its perihelion, 486

Heavens are void of any sensible resistance, 401, 445, 492; and, therefore, of almost any corporeal fluid whatever, 355, 356

“ suffer light to pass through them without any refraction, 485

Hydrostatics, the principles thereof delivered, 293